Question: Rewrite as a simplified fraction. ${2.\overline{28} = {?}}$
Solution: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}100x &= 228.2828...\\ 1x &= 2.2828...\end{align*}}$ Subtracting the two equations, we have: ${99x = 226}$ ${x = \dfrac{226}{99}} \text{or} {2 \dfrac{28}{99}}$